The News of the World's dominance over the Sunday Mirror dates back to 1999, save for the month of May 2000, according to the Audit Bureau of Circulations (ABC).
However, The Sun on Sunday lost 1.1% of its circulation between July and August, its sixth straight month of decline since it sold 3.2 million in its first week in February.
The 2,133,616 copies it shifted last month were more than half a million fewer than the News of the World managed, before it was closed in July 2011.
By contrast, the Sunday Mirror is now selling slightly more than it was then, after a 2.2% rise from July to 1,101,206 copies.
A Trinity Mirror spokesman put the rise down to the paper's Olympics coverage and an expose of Twitter paedophiles in one edition.
While The Sun on Sunday’s arrival in February took away the gains the Mirror had made in the absence of the News of the World, the £1 Trinity Mirror title has since stood firm against the onslaught from Rupert Murdoch’s 50p Sun.
In another sign that News International's iron grip on the Sunday market is loosening, the same shift in the relative circulations of The Sunday Times and The Sunday Telegraph occurred for the first time since July last year.
The former has outsold the latter by more than two to one in most months since the beginning of 2009.
With the two papers going head to head in their Olympic Games coverage, the Sunday Times registered its lowest circulation this year while the Sunday Telegraph registered its highest.
The Sunday Times slipped 0.5% on July to 914,685 copies, while The Sunday Telegraph added 1.6% to reach 463,733 copies.
At the overall market level, Sunday newspapers shifted only 0.3% more copies in August than in July, which as with the daily market, showed the lack of a hoped-for Olympic bounce.
This could be put down to seasonality, although last year the increase between July and August was 1.5%.
All Sunday papers lost circulation compared with August 2011.
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